A US green card shows you are a legal resident of the US. It doesn't identify your citizenship and it doesn't really mean anything to another country.
You didn't say what country your passport is from. That would make it easier to answer your questions. First I would suggest you use the internet to find out which countries Costa Rica require to have visas.
But that might not make any difference since Costa Rica requires all passports to have 6 months remaining until expiration.
From this link:
http://www.languagecourse.net/visa/costa_rica.php3
Required documents for visa:
(a) Completed application form.
(b) 2 passport-size photos.
(c) Passport valid for 6 months at time of entry.
(d) Proof of sufficient funds to cover duration of stay.
(e) Return or onward ticket.
Other links
http://costaricahomepages.com/acf981cde ... /visa.tmpl
http://costarica-embassy.org/
http://www.alfatravelguide.com/english/cr/cr-visa.htm
http://www.traveldocs.com/cr/vr.htm
http://www.learn4good.com/travel/costa_rica_visa.htm